scipy.linalg.

hankel#

scipy.linalg.hankel(c, r=None)[source]#

Construct a Hankel matrix.

The Hankel matrix has constant anti-diagonals, with c as its first column and r as its last row. If the first element of r differs from the last element of c, the first element of r is replaced by the last element of c to ensure that anti-diagonals remain constant. If r is not given, then r = zeros_like(c) is assumed.

The documentation is written assuming array arguments are of specified “core” shapes. However, array argument(s) of this function may have additional “batch” dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see Batched Linear Operations for details. Note that calls with zero-size batches are unsupported and will raise a ValueError.

Parameters:

carray_like: First column of the matrix.
rarray_like, optional: Last row of the matrix. If None, r = zeros_like(c) is assumed. r[0] is ignored; the last row of the returned matrix is [c[-1], r[1:]].

Returns:

A(len(c), len(r)) ndarray: The Hankel matrix. Dtype is the same as (c[0] + r[0]).dtype.

See also

toeplitz: Toeplitz matrix
circulant: circulant matrix

Examples

>>> from scipy.linalg import hankel
>>> hankel([1, 17, 99])
array([[ 1, 17, 99],
       [17, 99,  0],
       [99,  0,  0]])
>>> hankel([1,2,3,4], [4,7,7,8,9])
array([[1, 2, 3, 4, 7],
       [2, 3, 4, 7, 7],
       [3, 4, 7, 7, 8],
       [4, 7, 7, 8, 9]])